Central factor satisfies intermediate subgroup condition

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This article gives the statement, and possibly proof, of a subgroup property (i.e., central factor) satisfying a subgroup metaproperty (i.e., intermediate subgroup condition)
View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties
Get more facts about central factor |Get facts that use property satisfaction of central factor | Get facts that use property satisfaction of central factor|Get more facts about intermediate subgroup condition


Statement

Verbal statement

A central factor of a group is also a central factor in every intermediate subgroup.

Related facts

Generalizations and other particular cases of the generalizations

Related metaproperties for central factor

Proof

Using function restriction expressions

This subgroup property implication can be proved by using function restriction expressions for the subgroup properties
View other implications proved this way |read a survey article on the topic

This proof method generalizes to the following results: left-inner implies intermediate subgroup condition, left-extensibility-stable implies intermediate subgroup condition

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Proof using product with centralizer definition

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